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On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts  Towards Memetic Algorithms
, 1989
"... Short abstract, isn't it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers "...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could ..."
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Cited by 186 (10 self)
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Short abstract, isn't it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers "...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could possibly enumerate 10 9 tours per second on a computer it would thus take roughly 10 639 years of computing to establish the optimality of this tour by exhaustive enumeration." This quote shows the real difficulty of a combinatorial optimization problem. The huge number of configurations is the primary difficulty when dealing with one of these problems. The quote belongs to M.W Padberg and M. Grotschel, Chap. 9., "Polyhedral computations", from the book The Traveling Salesman Problem: A Guided tour of Combinatorial Optimization [124]. It is interesting to compare the number of configurations of realworld problems in combinatorial optimization with those large numbers arising in Cosmol...
Monte Carlo Methods for Tempo Tracking and Rhythm Quantization
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2003
"... We present a probabilistic generarive model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical score. The continuous hidden variables ..."
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Cited by 54 (9 self)
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We present a probabilistic generarive model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical score. The continuous hidden variables denote the tempo. We formulate two well known music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. Ex act computation of posterior features such as the MAP state is intractable in this model class, so we introduce Monte Carlo methods for integration and optimization. We compare Markov Chain Monte Carlo (MCMC) methods (such as Gibbs sampling, simulated annealing and iterative improvement) and sequential Monte Carlo methods (particle filters). Our simulation results suggest better results with sequential methods. The methods can be applied in both online and batch scenarios such as tempo tracking and transcription and are thus potentially useful in a number of music applications such as adaptive automatic accompaniment, score typesetting and music information retrieval.
Performance of a New Annealing Schedule
 Proc. 25th ACM/ IEEE DAC
, 1988
"... A new simulated annealing schedule has been developed; its application to the standard cell placement and the traveling salesman problems results in a two to twentyfour times speedup over annealing schedules clirrently available in the literature. Since it uses only statistical quantities, the annea ..."
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Cited by 32 (1 self)
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A new simulated annealing schedule has been developed; its application to the standard cell placement and the traveling salesman problems results in a two to twentyfour times speedup over annealing schedules clirrently available in the literature. Since it uses only statistical quantities, the annealing schedule is applicable to general combinatorial optimization problems. 1.
Adaptive Memory Programming: A Unified View of Metaheuristics
, 1998
"... The paper analyses recent developments of a number of memorybased metaheuristics such as taboo search, scatter search, genetic algorithms and ant colonies. It shows that the implementations of these general solving methods are more and more similar. So, a unified presentation is proposed under the ..."
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Cited by 27 (3 self)
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The paper analyses recent developments of a number of memorybased metaheuristics such as taboo search, scatter search, genetic algorithms and ant colonies. It shows that the implementations of these general solving methods are more and more similar. So, a unified presentation is proposed under the name of Adaptive Memory Programming (AMP). A number of methods recently developed for the quadratic assignment, vehicle routing and graph colouring problems are reviewed and presented under the adaptive memory programming point of view. AMP presents a number of interesting aspects such as a high parallelization potential and the ability of dealing with real and dynamic applications.
Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research
, 1999
"... This article briefly summarizes the work that has been done and presents the current standing of neural networks for combinatorial optimization by considering each of the major classes of combinatorial optimization problems. Areas which have not yet been studied are identified for future research. ..."
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Cited by 26 (0 self)
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This article briefly summarizes the work that has been done and presents the current standing of neural networks for combinatorial optimization by considering each of the major classes of combinatorial optimization problems. Areas which have not yet been studied are identified for future research.
Simulated Annealing with Extended Neighbourhood
, 1991
"... Simulated Annealing (SA) is a powerful stochastic search method applicable to a wide range of problems for which little prior knowledge is available. It can produce very high quality solutions for hard combinatorial optimization problems. However, the computation time required by SA is very large. V ..."
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Cited by 21 (14 self)
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Simulated Annealing (SA) is a powerful stochastic search method applicable to a wide range of problems for which little prior knowledge is available. It can produce very high quality solutions for hard combinatorial optimization problems. However, the computation time required by SA is very large. Various methods have been proposed to reduce the computation time, but they mainly deal with the careful tuning of SA's control parameters. This paper first analyzes the impact of SA's neighbourhood on SA's performance and shows that SA with a larger neighbourhood is better than SA with a smaller one. The paper also gives a general model of SA, which has both dynamic generation probability and acceptance probability, and proves its convergence. All variants of SA can be unified under such a generalization. Finally, a method of extending SA's neighbourhood is proposed, which uses a discrete approximation to some continuous probability function as the generation function in SA, and several impo...
Cut Size Statistics of Graph Bisection Heuristics
 SIAM JOURNAL ON OPTIMIZATION
, 1999
"... We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by “local” algorithms becomes peaked as the number ..."
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Cited by 20 (5 self)
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We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by “local” algorithms becomes peaked as the number of vertices in the graphs becomes large. Evidence is given that this distribution tends towards a Gaussian whose mean and variance scales linearly with the number of vertices of the graphs. Given the distribution of cut sizes associated with each heuristic, we provide a ranking procedure which takes into account both the quality of the solutions and the speed of the algorithms. This procedure is demonstrated for a selection of local graph bisection heuristics.
Extremal optimization: An evolutionary localsearch algorithm
 Computational Modeling and Problem Solving in the Networked World: Interfaces in Computer Science and Operations Research, Operations Research/Computer Science Interface Series
, 2003
"... Abstract A recently introduced generalpurpose heuristic for finding highquality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding farfromequilibrium phenomena in terms of selforganized criticality, a concept introduced to descr ..."
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Cited by 10 (0 self)
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Abstract A recently introduced generalpurpose heuristic for finding highquality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding farfromequilibrium phenomena in terms of selforganized criticality, a concept introduced to describe emergent complexity in physical systems. This method, called extremal optimization, successively replaces the value of extremely undesirable variables in a suboptimal solution with new, random ones. Large, avalanchelike fluctuations in the cost function selforganize from this dynamics, effectively scaling barriers to explore local optima in distant neighborhoods of the configuration space while eliminating the need to tune parameters. Drawing upon models used to simulate the dynamics of granular media, evolution, or geology, extremal optimization complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. It may be but one example of applying new insights into nonequilibrium phenomena systematically to hard optimization problems. This method is widely applicable and so far has proved competitive with – and even superior to – more elaborate generalpurpose heuristics on testbeds of constrained optimization problems with up to 10 5 variables, such as bipartitioning, coloring, and satisfiability. Analysis of a suitable model predicts the only free parameter of the method in accordance with all experimental results.
An ILP based hierarchical global routing approach for VLSI ASIC design
, 2007
"... The use of integrated circuits in highperformance computing, telecommunications, and consumer electronics has been growing at a very fast pace. The level of integration as measured by the number of logic gates in a chip has been steadily rising due to the rapid progress in processing and intercon ..."
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Cited by 5 (2 self)
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The use of integrated circuits in highperformance computing, telecommunications, and consumer electronics has been growing at a very fast pace. The level of integration as measured by the number of logic gates in a chip has been steadily rising due to the rapid progress in processing and interconnect technology. The interconnect delay in VLSI circuits has become a critical determiner of circuit performance. As a result, circuit layout is starting to play a more important role in today’s chip designs. Global routing is one of the key subproblems of circuit layout which involves finding an approximate path for the wires connecting the elements of the circuit without violating resource constraints. In this paper, several integer programming (ILP) based global routing models are fully investigated and explored. The resulting ILP problem is relaxed and solved as a linear programming (LP) problem followed by a rounding heuristic to obtain an integer solution. Experimental results obtained show that the proposed combined WVEM (wirelength, via, edge capacity) model can optimize several global routing objectives simultaneously and effectively. In addition, several hierarchical methods are combined with the proposed flat ILP based global router to reduce the CPU time by about 66 % on average for edge capacity model (ECM).
Integer Linear Programming Models for Global Routing
"... informs ® doi 10.1287/ijoc.1040.0127 © 2006 INFORMS Modern integrated circuit design involves the layout of circuits consisting of millions of switching elements or transistors. Due to the sheer complexity of the problem, optimizing the connectivity between transistors is very difficult. The circuit ..."
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Cited by 4 (1 self)
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informs ® doi 10.1287/ijoc.1040.0127 © 2006 INFORMS Modern integrated circuit design involves the layout of circuits consisting of millions of switching elements or transistors. Due to the sheer complexity of the problem, optimizing the connectivity between transistors is very difficult. The circuit interconnection is the single most important factor in performance criteria such as signal delay, power dissipation, circuit size, and cost. These factors dictate that interconnections, i.e., wires, be made as short as possible. The wireminimization problem is generally formulated as a sequence of discrete optimization subproblems that are known to be NPhard. Hence, they can only be solved approximately using metaheuristics. These methods are computationally expensive and the quality of the solution depends to a great extent on an appropriate choice of starting configuration and modeling techniques. In this paper, new modeling techniques are used to solve the routing problem formulated as an integer programming problem. The main contribution of this paper is a proposed global routing heuristic that combines the wire length, channel congestion, and number of pins in routes to find the best wiring layout of a circuit. By adding information such as channel congestion and the number of pins in each route as well as the wire length, the quality of the